Fundamental definition of capacitance: Is it correct to say that “the unit of capacitance is the farad; one farad stores one coulomb of charge,” without stating the voltage reference (i.e., per volt), given that 1 coulomb ≈ 6.24 × 10^18 electrons?

Introduction / Context:
Capacitance quantifies how much electric charge a capacitor stores per unit voltage across its plates. The SI unit is the farad (F). A common misconception is to define a farad simply as “one coulomb of charge,” which omits the critical dependence on voltage. This question tests whether the definition is understood precisely in terms of charge-per-volt and clarifies the role of the familiar conversion 1 coulomb ≈ 6.24 × 10^18 electrons.

Given Data / Assumptions:

• Capacitance C relates to charge Q and voltage V via C = Q / V.
• 1 coulomb ≈ 6.24 × 10^18 elementary charges (electrons).
• No leakage, ideal dielectric, and small-signal conditions are assumed for the definition.

Concept / Approach:
The correct definition is: a capacitor has capacitance C if it stores charge Q when a voltage V is applied, with C = Q / V. Therefore, 1 farad means the device stores 1 coulomb when 1 volt is applied (i.e., 1 F = 1 C per V). Saying “one farad stores one coulomb of charge” is incomplete and misleading because it ignores the required voltage reference of 1 volt. The electron count merely restates what 1 coulomb represents and does not alter the per-volt relationship.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional analysis confirms farad units are coulombs per volt (C/V). Any valid definition must include the voltage term. Manufacturer datasheets and textbooks consistently state 1 F = 1 C per V, reinforcing the necessity of the per-volt reference.

Why Other Options Are Wrong:
Correct: would only be true if it explicitly read “one coulomb per volt.”
Depends on the capacitor's ESR only: ESR affects loss, not the definition of units.
Cannot be determined: the SI definition is precise; no extra data are required.

Common Pitfalls:
Forgetting that stored charge scales with voltage; assuming “one coulomb” is absolute rather than per volt; confusing unit definitions with practical limitations like leakage or ESR.

Final Answer:
Incorrect